UNIQUAC Parameter Estimation 3

[tipu144]

Hi to All,

Happy New year to All of you..

Can anybody help me for determining the paratmeters of UNIQUAC equation? I want to use this equation for the prediction of experimental Heat of Mixing Data. This thing is new for me, so i want to start it from basic level..

Thanks
tipu

 

[siretb]

I perfectly respect your position, but I do not agree, as a end user of thermodynamics.
In theory, you are right.
I found the following link, that compares 3 methods.

http://www.aiche.org/uploadedFiles/Students/DepartmentUploads/thermodynamics.pdf

 

[UmeshMathur]

January 25, 2006
siretb:

While not disagreeing with most of Professor Suppes’ article that you referenced, I would make a simple point: Nowhere does he mention that use of NRTL for liquid systems suffers from the FUNDAMENTAL FLAW that the third interaction parameter (alpha) CANNOT be found from LLE data alone.

Therefore, I am skeptical about his blanket recommendations for LLE systems, preferring to rely instead my own study of the theory, backed by experience in numerous commercial applications.

I would suggest instead reliance on Professor John M. Prausnitz's numerous publications and books on the subject. Two good sources are:
(1) Prausnitz, Lichtenthaler, and Gomes de Azevedo: "Molecular Thermodynamics of Fuid Phase Equilibria" (3rd Edition, Prentice Hall, 1999). This is the most complete discussion of the theory to date.
(2) Prausnitz, et al, "Computer Calculations for Multicomponent Vapor-Liquid and Liquid-Liquid Equilibria" (Prentice Hall, 1980). This book discusses some significant theoretical and practical advantages for UNIQUAC over the earlier models.

As just about everyone in the business knows, Prausnitz is the pre-eminent authority on this subject, and the NRTL, UNIQUAC, and UNIFAC models were all developed under his supervision. Also, I would respectfully ask you to consider that if UNIQUAC did not have an outstanding theoretical basis, the UNIFAC group contribution method (which relies on the foundations laid by UNIQUAC) would not have achieved the outstanding success it has demonstrated for over 25 years. In fact, the originator (Professor Fredenslund) continued refining this method until his untimely death, and that work has been continued very ably by his successors (Rasmussen, Gani, and others at Lyngby, Denmark and Gmehling in Germany), to this day.

 

[tipu144]

Umeshmathur,

I am eagerly waiting for your reply.

thanks
tipu

 

[UmeshMathur]

tipu144:

I will revert to you this afternoon; sorry, I've been innundated with work.

 

[UmeshMathur]

tipu144:

For your problem, here's what I have:

You did not specify a system temperature. So, I assumed t=50 C.

I am assuming that you are using the "modified" UNIQUAC equation with the following:

Component 1 [Water]: r=0.92, q=1.4, q'=1.0
Component 2 [N-(2-Hydroxyethyl)ethylenediamine]: r=4.925, q=4.452, q'=4.452

On this basis, at a temperature of 50 C or 323.15 [Kelvin], for both infinite dilution activity coefficients=1 (ideal solution), the UNIQUAC parameters are:

a12 [Kelvin] = -346.3, a21 [Kelvin] = 634.4

Note: When the UNIQUAC parameters are pre-divided by R, the units become Kelvin. To convert the UNIQUAC parameter values quoted above to kcal/kgmol, multiply each of them by the value of R (1.987 kcal/kgmol/k). The units to use are dictated by the convention employed in your simulator.

I would hope that these values should give you a decent start for the regression you are performing.

If you need values at other temperatures, or if you are using the original UNIQUAC (i.e., the unmodified form where q = q' for all components), or you have other problems, let me know and I will re-run your cases.

 

[tipu144]

Umeshmathur,

Thank you very much.
Sorry I didn't mention about the temperature. The experimental data are available at 25, 40 and 50 degree C. Still there is a problem, I couldn't abtain a good result. I would like to inform you that I tried to solve it by adding temperature dependent parameters bij and bji, so that Taw12 = exp(a12 + b12/T) and Taw21 = exp(a21 + b21/T), and for the initial guess I just selected some random values for all the parameters, and I got better results compared to those with only a12 and a21, but still results are not satisfying me, so I believe that we need to do the same thing to get initial guess for b12 and b21 parameters as a12 and a21. So, If possible then could you please give me the detail information abt how to get initial values of all the four parameters (i.e. a12, a21, b12, and b21). If I will get this information then I think all the problems gonna be solve.

Thanks a lot
Tipu

 

[UmeshMathur]

tipu144:

You have 3 data points and so cannot estimate 4 parameters (a12, a21, b12, and b21). Unless you get more data, you need to stick to the simpler case with b12 and b21 both taken as zero.

Recall that UNIQUAC has a built-in temperature dependence for activity coefficients. If the results are not "satisfactory", and so you feel you must use 4 parameters, you have no choice but to get more experimental data.

 

[tipu144]

UmeshMathur:

Here I am providing you all of my experimental data of N-(2-Hydroxyethyl)ethylenediamine at 40 degree C. I am also providing the Predicted data with UNIQUAC equation with four parameters, and I got % AAD 3.02. My initial guesses for all four parameters were, a12=-1.568, a21=2.956, b12=254.26, and b21=-562.21 (All these values are random) and After Regression I got a12=-2.213, a21=-0.795, b12=625.098, and b21=317.663. Results are good, but as you know my all the initial guesses are random, thats why I am not sure about this predicted result.

x2 Hmixing(J/mol) UNIQUAC
0.0299 -936.3575 -881.1137
0.0498 -1316.8235 -1374.8295
0.0701 -1719.8516 -1814.6365
0.1000 -2338.4439 -2360.7882
0.1495 -3007.7829 -3042.9724
0.2002 -3620.2126 -3516.7523
0.2956 -4101.6374 -3959.3615
0.3547 -4234.0769 -4018.3230
0.3965 -4099.3087 -3984.5468
0.4461 -3919.7600 -3877.6126
0.4893 -3693.3327 -3733.8731
0.6009 -3175.7644 -3189.9575
0.6350 -3058.6137 -2983.4654
0.6723 -2669.1118 -2737.6165
0.7961 -1714.0532 -1810.2540

 

[UmeshMathur]

Tipu:

The fit looks fine to me. I didn't realize that you had many datasets. However, you should re-regress all data for all temperatures simultaneously.

(P.S.: I was in a hurry when I sent my post of 1 Feb, at 15:13 hrs.; I recommended putting b12 and b21 to zero, when I obviously should have said that a12 and a21 should be zeroed. Of course, now that isssue is no longer relevant as you can regress 4 parameters safely with all this data).

The initial guesses for the parameters are not important of the results show a good fit.

Best wishes.

Umesh

 

[tipu144]

UmeshMathur,

Thank you very very much for your kind help.

 

[UmeshMathur]

Tipu:

You are welcome, sir.

 

[dragonmark]

I read all the conversations here. I was just wondering why people go for heat of mixing data alone!!, anybody would like to make any comments on the applications of only heat of mixing data, because I am not sure that only heat of mixing data are effective for the predication of phase equilibria. What you think Umeshmathur, tipu144...?

 

[UmeshMathur]

dragonmark:

I agree with you, in that it is hard to imagine using heat of mixing data alone for commercial simulation work especially when phase equilibria may also be involved (tipu144's water-amine system). If heats of mixing are significant, my strong preference would be to regress UNIQUAC parameters using both VLE and heat of mxing data simultaneously. Also, a proper thermodynamic method for using calculated heats of mixing would need to be specified in the simulator.

Beyond that, I cannot comment as I am unaware of tipu144's application.